tailieunhanh - Báo cáo hóa học: " Research Article Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 407651 26 pages doi 2010 407651 Research Article Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings Daruni Boonchari1 and Satit Saejung2 1 Department of Mathematics Mahasarakham University Maha Sarakham 44150 Thailand 2 Department of Mathematics Khon Kaen University Khon Kaen 40002 Thailand Correspondence should be addressed to Satit Saejung saejung@ Received 22 June 2009 Revised 20 October 2009 Accepted 21 November 2009 Academic Editor Tomonari Suzuki Copyright 2010 D. Boonchari and S. Saejung. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed. 1. Introduction and Preliminaries Let C be a nonempty subset of a Banach space E and let T be a mapping from C into itself. When xn is a sequence in E we denote strong convergence of xn to x e E by xn x and weak convergence by xn x. We also denote the weak convergence of a sequence xn to x in the dual E by x n x . A point p e C is an asymptotic fixed point of T if there exists xn in C such that xn p and xn - Txn 0. We denote F T and F T by the set of fixed points and of asymptotic fixed points of T respectively. A Banach space E is said to be strictly convex if x yịị 2 1 for x y e S E z e E z 1 and x fy. It is also said to be uniformly convex if for